A010133 Continued fraction for sqrt(41).

6, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			6.40312423743284868648821767... = 6 + 1/(2 + 1/(2 + 1/(12 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 05 2009
		

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• G. Xiao, Contfrac
• Index entries for continued fractions for constants
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A010495 (decimal expansion).

Cf. A041068/A041069 (convergents), A248267 (Egyptian fraction).

Programs

Mathematica

ContinuedFraction[Sqrt[41],300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

PARI

{ allocatemem(932245000); default(realprecision, 25000); x=contfrac(sqrt(41)); for (n=0, 20000, write("b010133.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009

Formula

From Elmo R. Oliveira, Aug 03 2024: (Start)

G.f.: 2*(3 + x + x^2 + 3*x^3)/((1 - x)*(1 + x + x^2)).

a(n) = a(n-3), n > 3. (End)